Genesis 6 tells us this of the days before Noah’s Flood: “Now it came to pass, when men began to multiply on the face of the earth, and daughters were born to them, that the sons of God saw the daughters of men, that they were beautiful; and they took wives for themselves of all whom they chose … There were giants on the earth in those days, and also afterward, when the sons of God came in to the daughters of men and they bore children to them. Those were the mighty men who were of old, men of renown” (Genesis 6:1-2 Genesis 6:1-2  And it came to pass, when men began to multiply on the face of the earth, and daughters were born to them,
 That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.
American King James Version×; Genesis 6:4 Genesis 6:4There were giants in the earth in those days; and also after that, when the sons of God came in to the daughters of men, and they bore children to them, the same became mighty men which were of old, men of renown.
American King James Version×).
Some have taught that this refers to fallen angels interbreeding with human women to produce half-demon giants. But there’s a more rational explanation.
Halley’s Bible Handbook, a popular study resource, states that “the ‘sons of God’ (v. 2) are thought to have been either fallen angels … or leaders in Sethite families [those descended from Adam’s son Seth] who intermarried with godless descendants of [Adam’s son] Cain” (25th ed., 2000, p. 96).
The first possibility offered here is not really a possibility at all, even though angels are referred to as “sons of God” in Job 38:7 Job 38:7When the morning stars sang together, and all the sons of God shouted for joy?
American King James Version×because God is their “Father” through creation. Angels are spirit beings (Hebrews 1:7 Hebrews 1:7And of the angels he said, Who makes his angels spirits, and his ministers a flame of fire.
American King James Version×), not fleshly creatures. They neither marry nor sexually reproduce (Luke 20:34-36 Luke 20:34-36  And Jesus answering said to them, The children of this world marry, and are given in marriage:  But they which shall be accounted worthy to obtain that world, and the resurrection from the dead, neither marry, nor are given in marriage:  Neither can they die any more: for they are equal to the angels; and are the children of God, being the children of the resurrection.
American King James Version×). Also, this explanation would violate the principle made clear in Genesis 1 that each living kind reproduces only “according to its kind.” Furthermore, the risen Jesus explained that fallen angels, or demons, are not able to manifest themselves materially like He and the righteous angels can (Luke 24:39 Luke 24:39Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit has not flesh and bones, as you see me have.
American King James Version×; compare 24:40-43; Genesis 18:1-8 Genesis 18:1-8  And the LORD appeared to him in the plains of Mamre: and he sat in the tent door in the heat of the day;  And he lift up his eyes and looked, and, see, three men stood by him: and when he saw them, he ran to meet them from the tent door, and bowed himself toward the ground,  And said, My LORD, if now I have found favor in your sight, pass not away, I pray you, from your servant:  Let a little water, I pray you, be fetched, and wash your feet, and rest yourselves under the tree:  And I will fetch a morsel of bread, and comfort you your hearts; after that you shall pass on: for therefore are you come to your servant. And they said, So do, as you have said.  And Abraham hastened into the tent to Sarah, and said, Make ready quickly three measures of fine meal, knead it, and make cakes on the hearth.  And Abraham ran to the herd, and fetched a calf tender and good, and gave it to a young man; and he hurried to dress it.  And he took butter, and milk, and the calf which he had dressed, and set it before them; and he stood by them under the tree, and they did eat.
American King James Version×, Genesis 18:16 Genesis 18:16And the men rose up from there, and looked toward Sodom: and Abraham went with them to bring them on the way.
American King James Version×; Genesis 19:1 Genesis 19:1And there came two angels to Sodom at even; and Lot sat in the gate of Sodom: and Lot seeing them rose up to meet them; and he bowed himself with his face toward the ground;
American King James Version×). Rather, we see demons in Scripture only possessing individuals or appearing as ghostly apparitions.
The second explanation in Halley’s is far more reasonable. Genesis 4 gives the story of Cain and Abel and follows with the genealogical descent from Cain. Genesis 5 is called “the book of the genealogy of Adam” (Genesis 5:1 Genesis 5:1This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him;
American King James Version×). It starts with God’s creation of Adam and how Adam’s line continued through Seth. As with the angels, Adam was a “son of God” by creation (compare Luke 3:38 Luke 3:38Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God.
American King James Version×)—though even more so since Adam was made in God’s image (Genesis 1:26 Genesis 1:26And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creeps on the earth.
American King James Version×; Genesis 5:1-3 Genesis 5:1-3  This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him;  Male and female created he them; and blessed them, and called their name Adam, in the day when they were created.  And Adam lived an hundred and thirty years, and begat a son in his own likeness, and after his image; and called his name Seth:
American King James Version×). Of this family line through Seth it is stated, “Then men began to call on the name of the Lord” (Genesis 4:26 Genesis 4:26And to Seth, to him also there was born a son; and he called his name Enos: then began men to call on the name of the LORD.
American King James Version×)—which could also be rendered “… began to be called after the name of the Lord.” Then, in the next chapter, Genesis 6, we see “the sons of God” (men of Seth’s godly line in this explanation) intermarrying with “the daughters of men” (women of Cain’s ungodly line).
There is also another sensible way to understand what Genesis 6 is describing, in which the phrase rendered “sons of God” should actually be translated “sons of the gods,” as the Hebrew word elohim here, plural in form, can sometimes refer to false gods instead of the true God. In this explanation, wicked men referred to as sons of the gods (either pagan worshippers or perhaps men purported to be demigods, as ancient rulers often claimed of themselves) forcibly “took” innocent women as wives—an example perhaps of the evil conduct of the day.
In any event, human beings were clearly the problem here—not angels. God says amid the verses of Genesis 6 quoted above, “My Spirit shall not strive with man forever” (Genesis 6:3 Genesis 6:3And the LORD said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.
American King James Version×) and “I will destroy man whom I have created from the face of the earth” (Genesis 6:7 Genesis 6:7And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repents me that I have made them.
American King James Version×). Thus, the “giants” mentioned must have been human also—descendants of Adam and Eve (compare Acts 17:26 Acts 17:26And has made of one blood all nations of men for to dwell on all the face of the earth, and has determined the times before appointed, and the bounds of their habitation;
American King James Version×).
It’s possible that the word translated “giants” here, nephilim—from a root meaning to fall or make to fall—could refer to tyrants. But the word is used of people of giant stature later in Numbers 13:33 Numbers 13:33And there we saw the giants, the sons of Anak, which come of the giants: and we were in our own sight as grasshoppers, and so we were in their sight.
American King James Version×. So the very powerful, and possibly very tall, people of Genesis 6 were destroyed in the Flood. But there would be other giants following the Flood, who were descended, just as everyone else in the post-Flood world, from Noah—again, not angels (compare Deuteronomy 2:20-21 Deuteronomy 2:20-21  (That also was accounted a land of giants: giants dwelled therein in old time; and the Ammonites call them Zamzummims;  A people great, and many, and tall, as the Anakims; but the LORD destroyed them before them; and they succeeded them, and dwelled in their stead:
American King James Version×; Deuteronomy 3:11 Deuteronomy 3:11For only Og king of Bashan remained of the remnant of giants; behold his bedstead was a bedstead of iron; is it not in Rabbath of the children of Ammon? nine cubits was the length thereof, and four cubits the breadth of it, after the cubit of a man.
American King James Version×). Consider Goliath, whom David slew. He was more than nine feet tall (1 Samuel 17:4 1 Samuel 17:4And there went out a champion out of the camp of the Philistines, named Goliath, of Gath, whose height was six cubits and a span.
American King James Version×). But he was still just a man (1 Samuel 17:24-25 1 Samuel 17:24-25  And all the men of Israel, when they saw the man, fled from him, and were sore afraid.  And the men of Israel said, Have you seen this man that is come up? surely to defy Israel is he come up: and it shall be, that the man who kills him, the king will enrich him with great riches, and will give him his daughter, and make his father’s house free in Israel.
American King James Version×; 1 Samuel 17:33 1 Samuel 17:33And Saul said to David, You are not able to go against this Philistine to fight with him: for you are but a youth, and he a man of war from his youth.
American King James Version×)—not some human-demonic hybrid.